Finding cuts and separators is a classical topic of combinatorial
optimization and in recent years there has been an increase in
interest in the fixed-parameter tractability of such problems
[1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
Recall that a problem is fixed-parameter tractable (or FPT) with
respect to a parameter \(k\)  if it can be solved in time \(f(k)\cdot n^{O(1)}\)  for
some function \(f(k)\)  depending only on \(k\) 
[9]}, [10]}, [11]}. In typical parameterized
separation problems, the parameter \(k\)  is the size of the separator we
are looking for, thus fixed-parameter tractability with respect to
this parameter means that the combinatorial explosion is restricted to
the size of the separator, but otherwise the running time depends
polynomially on the size of the graph.
